| Topological insulator is a state of matter with novel quantum properties,which has attracted widespread attention in the fields of condensed matter physics and material science.Different from ordinary insulators,topological insulators have topologically pro-tected edge states or surface states without band gaps on their edges or surfaces.These edge states or surface states are not affected by non-magnetic impurities and perturbations.Two typical one-dimensional(1D)topological insulators and topological superconductor models are Su-Schrieffer-Heeger(SSH)model of polyacetylene and Kitaev model with p-wave superconducting pairing terms.Both models describe 1D non-interacting spin-less standard tight-binding system.Although these two models are relatively simple,they both show rich physical properties.We usually use topological invariants(Z or Z2)to characterize the properties of topological systems.Different topological invariants represent different topological effects.Different topological invariants can describe topo-logical quantum phase transitions.In recent years,researches have shown that topological insulators will exhibit some novel phenomena and have good application prospects in spintronics and quantum computers.One of the unique features of a non-Hermitian sys-tem is the violation of conservation law of the Dirac probability,based on which,complex potentials are used to describe the phenomena of open systems.Although a class of system with parity-time(PT-)symmetry is non-Hermitian,the system has a pure real energy spectrum in certain parameter regions,which has aroused great research interest,especially the topological properties of such systems have been extensively studied.In addition,a compound topological system composed of simple tight-binding chains,the ladder system,has become the best choice for studying various physical behaviors and topological properties in recent years.For example,people have studied a ladder system composed of two coupled SSH chains,a ladder system composed of two coupled Kitaev chains,and a ladder system which are composed of a SSH chain coupled with a Kitaev chain.The coupled SSH systems,as the crossover from 1D to two-dimensional(2D)system,host a variety of physical phenomena which are diferent from that of both 1D and 2D systems.In this thesis,we devote to the simulation and study of three coupled SSH chains,and the main contents are as follows:Based on the three coupled SSH chains,we study the effects of the position of the defect terms on the spontaneous PT-symmetry-breaking behavior under three different cases in coupled SSH chains whose Hermiticity is broken by the presence of two conju-gated imaginary potentials ±iγ(defect terms).We analyze and discuss the energy spectra and PT symmetry in the topologically trivial and topologically nontrivial regimes under three different cases in detail;that is,the defect terms are located at the two end positions,the middle positions,and each position in the coupled SSH chains,respectively.We show that the defect terms located at different positions in the system have significant impacts on the energy spectra in topologically trivial and nontrivial regions.Meanwhile,we find that the topologically nontrivial zero-energy edge modes exist in PT symmetric region and the system undergoes several PT-symmetry-breaking transitions when the defect terms are located at the middle positions.Interestingly,when the defect terms are located at each position,the PT symmetry of the system is always spontaneously broken no matter how the loss rate γ changes.Under the same parameter regimes,furthermore,the energy spectra of the system for the cases that the defect terms are located at the two end positions and at the middle positions are more robust than to the case that the defect terms are located at each position. |
